Projective dimension of weakly chordal graphic arrangements

Autor: Abe, Takuro, Kühne, Lukas, Mücksch, Paul, Mühlherr, Leonie

A graphic arrangement is a subarrangement of the braid arrangement whose set of hyperplanes is determined by an undirected graph. A classical result due to Stanley, Edelman and Reiner states that a graphic arrangement is free if and only if the corre

Externí odkaz: http://arxiv.org/abs/2307.06021

A basis construction of the extended Catalan and Shi arrangements of the type $A_{2}$

Autor: Abe, Takuro, Suyama, Daisuke

In [9], Terao proved the freeness of multi-Coxeter arrangements with constant multiplicities by giving an explicit construction of bases. Combining it with algebro-geometric method, Yoshinaga proved the freeness of the extended Catalan and Shi arrang

Externí odkaz: http://arxiv.org/abs/1312.5524

The Shi arrangements and the Bernoulli polynomials

Autor: Suyama, Daisuke, Terao, Hiroaki

Publikováno v: Bulletin of London Mathematics Society, 44 (2012), 563-570

The braid arrangement is the Coxeter arrangement of the type $A_\ell$. The Shi arrangement is an affine arrangement of hyperplanes consisting of the hyperplanes of the braid arrangement and their parallel translations. In this paper, we give an expli

Externí odkaz: http://arxiv.org/abs/1103.3214

Bases for the derivation modules of two-dimensional multi-Coxeter arrangements and universal derivations

Autor: Wakamiko, Atsushi

Publikováno v: Tokyo J. of Math. 30, 1 (2007), 99-116

Let $\A$ be an irreducible Coxeter arrangement and $\bfk$ be a multiplicity of $\A$. We study the derivation module $D(\A, \bfk)$. Any two-dimensional irreducible Coxeter arrangement with even number of lines is decomposed into two orbits under the a

Externí odkaz: http://arxiv.org/abs/1010.5266

The freeness of Ish arrangements

Autor: Shuhei Tsujie, Daisuke Suyama, Takuro Abe

Publikováno v: Discrete Mathematics and Theoretical Computer Science
27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), Jul 2015, Daejeon, South Korea. pp.273-284

The Ish arrangement was introduced by Armstrong to give a new interpretation of the $q; t$-Catalan numbers of Garsia and Haiman. Armstrong and Rhoades showed that there are some striking similarities between the Shi arrangement and the Ish arrangemen

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c8cd924ca323c5101420bf582d4e53a5